AN ELEMENTARY TREATISE ON ANALYTIC MECHANICS

By J. MIANM

CONTENTS INTRODUCTION THE OBJECTS OF OUR ENQUIRY SYMMETRY AND EVOLUTION TRANSFORMING STRUCTURES TIME REGAINED DIRECTED TIME ORDERING AND TIME’S ARROW PART I NATURAL PHILOSOPHY OF TIME ON NEWTON ON TIME ON NEWTON’S METHODOLOGY IN THE SCHOLIUM THE TRIPARTITE NATURE OF NEWTONIAN TIME WAS NEWTON A FUNCTIONALIST ABOUT TIME? CHAPTER SUMMARY ON LEIBNIZ ON TIME LEIBNIZ’S METAPHYSICS OF TIME THE CHRONORDINAL PROBLEM THE CHRONOMETRIC PROBLEM ON MACH ON TIME MACH’S PHILOSOPHICAL OUTLOOK THE EARLY MACHIAN VIEW OF TIME INERTIAL CLOCKS MACHIAN TENSIONS PART II SYMMETRY AND STRUCTURE STRUCTURE AND POSSIBILITY CONSTITUTIVE STRUCTURE AND KINEMATICAL POSSIBILITY NOMIC STRUCTURE AND DYNAMICAL EQUIVALENCE SYMMETRY AND EQUIVALENCE CONSERVATION AND GEOMETRY CANONICAL MECHANICS CONTACT MECHANICS CONSERVED CHARGES AND SYMMETRIES ISOLATED SUBSTRUCTURES AND NARROW SYMMETRIES NOMIC STRUCTURE OF NEWTONIAN MECHANICS IRREGULAR NOMIC STRUCTURE IRREGULAR LAGRANGIANS CONSTRAINED HAMILTONIAN MECHANICS DIRAC’S THEOREM NOETHER’S SECOND THEOREM DIAGNOSING DYNAMICAL REDUNDANCY VARIATIONAL SYMMETRIES OF HISTORIES NOETHER’S SECOND THEOREM REVISED INITIAL VALUE CONSTRAINTS DYNAMICAL REDUNDANCY NOMIC STRUCTURE OF BARBOUR–BERTOTTI THEORY THE NEW FRAMEWORK THE AIR CLASSI?CATION THE NOMIC-AIR ANALYSIS GLOBAL AND LOCAL STRUCTURES PART III THE PROBLEM OF TIME IN CLASSICAL MECHANICS 10 SPATIOTEMPORAL STRUCTURE AND THEORY RE-ARTICULATION 10 1 STRUCTURES AND HEURISTICS 10 2 SPATIOTEMPORAL STRUCTURE IN NEWTONIAN MECHANICS 10 3 SPATIOTEMPORAL STRUCTURE IN BARBOUR–BERTOTTI THEORY 10 4 CHAPTER SUMMARY 11 LOCAL TEMPORAL SYMMETRY 11 1 TIME REPARAMETERIZATION INVARIANCE 11 2 DYNAMICAL REDUNDANCY AND EVOLUTION 11 3 TEMPORAL LEIBNIZ SHIFTS 11 4 CHAPTER SUMMARY 12 REPARAMETERIZATION INVARIANT DYNAMICS 12 1 JACOBI ACTIONS AS GEODESIC PRINCIPLES ON CON?GURATION SPACE 12 2 TOTAL ENERGY AS A CONSTANT OF MOTION 12 3 GENERALIZED HAMILTON–JACOBI FORMALISM 12 4 INTEGRALS OF MOTION AND COMPLETE OBSERVABLES 12 5 CHAPTER SUMMARY 13 TEMPORAL STRUCTURE REGAINED 13 1 DI?ERENTIATING DYNAMICAL REDUNDANCY AND EVOLUTION 13 2 A DYNAMICAL VIEW OF HAMILTONIAN CONSTRAINTS CONTENTS 13 3 THE STRUCTURE OF JACOBI THEORIES 13 4 CHAPTER SUMMARY 14 CONCLUSION AND PROSPECTUS 14 1 THE PROBLEM OF TIME IN CLASSICAL MECHANICS 14 2 QUANTIZATION AND REDUNDANCY 14 3 GRAVITATION AND REFOLIATION 14 4 THE TWO FACES OF CLASSICAL GRAVITY 14 5 RELATIONAL QUANTIZATION AND THE NEW COPERNICAN PRINCIPLE 14 6 RESOLVING THE BIG BANG REFERENCES